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Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

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Example Questions

Example Question #26 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$19\pi\textup{ in}^2$

$18\pi\textup{ in}^2$

$15\pi\textup{ in}^2$

$16\pi\textup{ in}^2$

$17\pi\textup{ in}^2$

Correct answer:

$16\pi\textup{ in}^2$

Explanation:

In order to solve this problem, we need to recall the formula for the area of a circle:

$A= r^2\pi$

The circle in this question provides us with the diameter, so we first have to solve for the radius. Remember, the radius is half the diameter:

$r=\frac{d}{2}$

$r=\frac{8}{2}$

r=4

Now that we have the radius we can use the formula to solve:

$A=4^2\pi$

Solve:

$A=16\pi\textup{ in}^2$

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Example Question #1 : Circumference Of A Circle

What is the circumference of a circle with a radius equal to ?

Possible Answers:

$196\pi$

$14\pi$

$7\pi$

$49\pi$

Correct answer:

$14\pi$

Explanation:

The circumference can be solved using the following equation:

$C=2r\pi=2(7)\pi=14\pi$

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Example Question #1 : Circumference Of A Circle

The radius of a circle is t^2 . Give the circumference of the circle in terms of .

Possible Answers:

$2\pi t^2$

$\pi t$

$4\pi t^2$

$\pi t^2$

$2\pi t$

Correct answer:

$2\pi t^2$

Explanation:

The circumference can be calculated as $Circumference =2\pi r$ , where is the radius of the circle.

$Circumference =2\pi r=2\pi t^2$

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Example Question #2 : Circumference Of A Circle

What is the circumference of a circle with a radius of ?

Possible Answers:

$16\pi$

$16\pi^{2}$

$28\pi$

$8\pi$

Correct answer:

$16\pi$

Explanation:

The circumference can be solved using the following equation:

$C=2r\pi$

Where represents the radius. Therefore, when we substitute our radius in we get:

$=2(8)\pi =16\pi$

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Example Question #1 : How To Find Circumference

If this circle has a diameter of 12 inches, what is its circumference?

Circle_12d

Possible Answers:

$12\pi\ \text{inches}$

$44\ \text{inches}$

$38\ \text{inches}$

$6\pi\ \text{inches}$

none of these

Correct answer:

$12\pi\ \text{inches}$

Explanation:

Know that the formula for circumference is $C=D\pi$ , where C is the circumference and D is the diameter. It is given that the diameter is 12 inches. Therefore, the circumference is $C=12\pi \hspace\ \text{inches}$

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Example Question #1 : Circumference Of A Circle

If a circle has an area of $81\pi$ , what is the circumference of the circle?

Possible Answers:

$27\pi$

$90\pi$

$18\pi$

$81\pi$

$9\pi$

Correct answer:

$18\pi$

Explanation:

The formula for the area of a circle is πr². For this particular circle, the area is 81π, so 81π = πr². Divide both sides by π and we are left with r²=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

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Example Question #2 : Circumference Of A Circle

If a circle has an area of $16\pi \; in^{2}$ , what is the circumference?

Possible Answers:

$10\pi \; in$

$12\pi \; in$

$4\pi \; in$

$6\pi \; in$

$8\pi \; in$

Correct answer:

$8\pi \; in$

Explanation:

For a circle, the formula for area is $A = \pi r^{2}$ and the formula for circumference is $C=\pi d$ , where is the radius and is the diameter.

Plug the known quantities into the area formula and solve for the radius:

$16\pi =\pi r^{2}$

$r=4\; in$

Now plug this value into the circumference formula to solve:

$C = \pi d = \pi 2r = \pi 2(4) = 8\pi\; in$

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Example Question #2 : Circumference Of A Circle

Find the circumference of a circle with a radius of .

Possible Answers:

$4\pi$

$\pi$

$2\pi$

$6\pi$

Correct answer:

$4\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 2 \times\pi$

Solve.

$\text{Circumference}=4\times \pi$

Simplify.

$\text{Circumference}=4\pi$

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Example Question #5 : Circumference Of A Circle

Find the circumference of a circle that has a radius of $\frac{1}{2}$ .

Possible Answers:

$\frac{1}{2}\pi$

$\pi$

$2\pi$

$-\pi$

Correct answer:

$\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times \frac{1}{2} \times\pi$

Solve.

$\text{Circumference}=\frac{2}{2} \times\pi$

Simplify.

$\text{Circumference}= \pi$

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Example Question #3 : Circumference Of A Circle

Find the circumference of the circle with a radius of .

Possible Answers:

$5\pi$

$100\pi$

$20\pi$

$10\pi$

Correct answer:

$20\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 10 \times\pi$

Solve.

$\text{Circumference}=20\times\pi$

Simplify.

$\text{Circumference}=20\pi$

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Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #26 : Area Of A Circle

Example Question #1 : Circumference Of A Circle

Example Question #1 : Circumference Of A Circle

Example Question #2 : Circumference Of A Circle

Example Question #1 : How To Find Circumference

Example Question #1 : Circumference Of A Circle

Example Question #2 : Circumference Of A Circle

Example Question #2 : Circumference Of A Circle

Example Question #5 : Circumference Of A Circle

Example Question #3 : Circumference Of A Circle

All Common Core: 7th Grade Math Resources

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